Causality is the process by which the behaviour of one state (the cause) influences another state (the effect).
Many systems posses a spatially causal structure where each state depends only on `upstream' states and
are unaffected by `downstream' states.
Specifically, we may express the \(j\) th state as a function of the \(n-j\)  upstream states only:
\(y_{j} = f(x_j, \, x_{j+1}, \, \dots \, x_n)\) .
For example, \(y_n\)  depends only on \(x_n\)  whereas \(y_1\)  depends only all the elements of \(x\) .
Accordingly, if we know that the system at hand possesses a spatially causal structure
we may seek a piDMD model that is upper triangular.
Such structures are typical of a system with causal features,
for example, time-delay coordinates [1]}, feed-forward/strict-feedback
systems [2]}, [3]}, and other control systems [4]}.
